Question

a person going to a party was asked to bring 4 different bags of chips. going to the store, she finds 17 varieties. how many different selections can she make? question help: video submit question jump to answer

Explanation:

Step1: Identify the problem type

This is a combination problem since the order of selecting the chip bags does not matter. The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 17 \) (total varieties) and \( k = 4 \) (number of bags to select).

Step2: Calculate factorials

First, calculate \( n!=17! = 17\times16\times15\times14\times13\times\cdots\times1 \), \( k!=4! = 4\times3\times2\times1=24 \), and \( (n - k)!=(17 - 4)!=13! = 13\times12\times\cdots\times1 \).

Step3: Simplify the combination formula

\( C(17, 4)=\frac{17!}{4!(17 - 4)!}=\frac{17\times16\times15\times14\times13!}{4!\times13!} \). The \( 13! \) terms cancel out. Then we have \( \frac{17\times16\times15\times14}{4\times3\times2\times1} \).

Step4: Compute the numerator and denominator

Numerator: \( 17\times16\times15\times14 = 17\times16\times210=17\times3360 = 57120 \)
Denominator: \( 4\times3\times2\times1 = 24 \)
Then \( \frac{57120}{24}=2380 \)

Answer:

2380